a28c1ff5-e7b3-4941-938a-acac115e571a 297 4 5 false false 0 decimal

&[DATE] &[TIME] - &[FILENAME]

Oppdragsnr.:

Oppdragsnavn:

Beregningsnr.:

Emne: Ståltemperaturer ved brann

Utarbeidet:

Kontrollert:

Nidaros Byggkompetanse AS

TOPPTEKST

NS-EN 1991-1-2:2002+NA:2008 & NS-EN 1993-1-2:2005+NA:2009

Eksempelet er en HEA360 som har konturisolasjon, 3 sidig eksponering ratio.Ap_V blir derfor det samme som ratio.Am_V

d.p 0.01 :

ρ.p 350 :

c.p 1200 :

λ.p 0.12 :

THESE ARE THE VALUES USED IN THE EXAMPLE I'M TRYING TO MIMIC

ratio.Ap_V 107102^* :

INNDATA

Densitet stål ρ.a 7850 :

Standard temperatur-tidkurve t θ.g 203458 t * 1 + log10 * + :

t Δθ.g 34588 t * 1 + (10 ln * / * :

I HAVE MANUALLY DERIVATED θg(t) TO GET THIS EXPRESSION.. MAYBE THERES ANOTHER WAY..?

θ.a φ c.p ρ.p * θ.a c.a 1 el ρ.a * / d.p * ratio.Ap_V * c.p ρ.p * θ.a c.a 2 el ρ.a * / d.p * ratio.Ap_V * c.p ρ.p * θ.a c.a 3 el ρ.a * / d.p * ratio.Ap_V * c.p ρ.p * θ.a c.a 4 el ρ.a * / d.p * ratio.Ap_V * 41 mat :

SYSTEM AV DIFFERENSIALLIGNINGER

θ.a c.a 425 7.73 101^/ θ.a * + 1.69 103^/ θ.a 2^* - 2.22 106^/ θ.a 3^* + 66613002738 θ.a - / + 54517820 θ.a 731 - / + 65041 mat :

I CANT GET THIS CONFIGURATION OF THE EXPRESSION TO WORK. I LOCATED THE ERROR TO e^φ.

t θ.a D λ.p ratio.Ap_V * d.p θ.a c.a 1 el * ρ.a * 1 θ.a φ 1 el 3 / + (* / t θ.g θ.a - (* e θ.a φ 1 el 10 / (^1 - (t Δθ.g * - λ.p ratio.Ap_V * d.p θ.a c.a 2 el * ρ.a * 1 θ.a φ 2 el 3 / + (* / t θ.g θ.a - (* e θ.a φ 2 el 10 / (^1 - (t Δθ.g * - λ.p ratio.Ap_V * d.p θ.a c.a 3 el * ρ.a * 1 θ.a φ 3 el 3 / + (* / t θ.g θ.a - (* e θ.a φ 3 el 10 / (^1 - (t Δθ.g * - λ.p ratio.Ap_V * d.p θ.a c.a 4 el * ρ.a * 1 θ.a φ 4 el 3 / + (* / t θ.g θ.a - (* e θ.a φ 4 el 10 / (^1 - (t Δθ.g * - 41 mat :

t θ.a D λ.p ratio.Ap_V * d.p θ.a c.a 1 el * ρ.a * 1 θ.a φ 1 el 3 / + (* / t θ.g θ.a - (* e 0.1 10 / (^1 - (t Δθ.g * - λ.p ratio.Ap_V * d.p θ.a c.a 2 el * ρ.a * 1 θ.a φ 2 el 3 / + (* / t θ.g θ.a - (* e 0.1 10 / (^1 - (t Δθ.g * - λ.p ratio.Ap_V * d.p θ.a c.a 3 el * ρ.a * 1 θ.a φ 3 el 3 / + (* / t θ.g θ.a - (* e 0.1 10 / (^1 - (t Δθ.g * - λ.p ratio.Ap_V * d.p θ.a c.a 4 el * ρ.a * 1 θ.a φ 4 el 3 / + (* / t θ.g θ.a - (* e 0.1 10 / (^1 - (t Δθ.g * - 41 mat :

INITIALBETINGELSER OG LØSNING AV DIFFERENSIALLIGNINGER

θ.a.init 20 :

θ.a.12 600 :

θ.a.23 735 :

θ.a.34 900 :

steps 5 :

t.init 0 :

t.12 147.6 :

t.23 204.5 :

t.34 289.4 :

t.final 360 :

θ.a ca 425 7.73 101^/ θ.a * + 1.69 103^/ θ.a 2^* - 2.22 106^/ θ.a 3^* + θ.a 600 ≤ 66613002738 θ.a - / + θ.a 600735 ltle 54517820 θ.a 731 - / + θ.a 735900 ltle 650 cases :

res θ.a.init t.init t.12 steps t.12 t.init - (* t θ.a D 1 el dn_GearsBDF θ.a.12 t.12 t.23 steps t.23 t.12 - (* t θ.a D 2 el dn_GearsBDF θ.a.23 t.23 t.34 steps t.34 t.23 - (* t θ.a D 3 el dn_GearsBDF θ.a.34 t.34 t.final steps t.final t.34 - (* t θ.a D 4 el dn_GearsBDF 41 mat :

x ca x 0 1200 lele /

θ.a t.12 res 1 el 2 col res 1 el 1 col θ.a ainterp :

θ.a.12 t.12 147.955776

θ.a t.23 res 2 el 2 col res 2 el 1 col θ.a ainterp :

θ.a.23 t.23 204.548984

735 ca 5000

θ.a t.34 res 3 el 2 col res 3 el 1 col θ.a ainterp :

θ.a.34 t.34 289.462216

check t.12 θ.a.12 t.12 - abs 1105 -^* < t12 er tilstrekkelig itterert For stort avvik på t12 if t.23 θ.a.23 t.23 - abs 1105 -^* < t23 er tilstrekkelig itterert For stort avvik på t23 if t.34 θ.a.34 t.34 - abs 1105 -^* < t34 er tilstrekkelig itterert For stort avvik på t34 if 31 mat : For stort avvik på t12 For stort avvik på t23 For stort avvik på t34 31 mat

θ.a phi c.p ρ.p * θ.a c.a 1 el ρ.a * / d.p * ratio.Ap_V * θ.a 600 ≤ c.p ρ.p * θ.a c.a 2 el ρ.a * / d.p * ratio.Ap_V * θ.a 600735 ltle c.p ρ.p * θ.a c.a 3 el ρ.a * / d.p * ratio.Ap_V * θ.a 735900 ltle c.p ρ.p * θ.a c.a 4 el ρ.a * / d.p * ratio.Ap_V * cases :

FJERNING AV DUPLIKATVERDIER I OVERGANGER OG SAMMENSTILLING NY ENHETLIG LØSNING

res.stripped res 1 el 1 res 1 el rows 1 - 12 submatrix res 2 el 1 res 2 el rows 1 - 12 submatrix res 3 el 1 res 3 el rows 1 - 12 submatrix res 4 el 41 mat :

x phi x 0 1200 lele /

20 phi 13.0169

735 phi 1.145

res.stacked res.stripped 1 el res.stripped 2 el res.stripped 3 el res 4 el stack :

FUNKSJONSUTTRKK VED INTERPOLERING AV ENHETLIG LØSNING

θ.a.cr t res.stacked 2 col res.stacked 1 col θ.a.cr ainterp :

t.req θ.a res.stacked 1 col res.stacked 2 col t.req ainterp :

e x phi ( 10 / ^ 1 - x 0 1200 lele /

θ.a.cr 650 :

-->

θ.a.cr t 165.43

t.req 60 :

-->

t.req θ.a 277.59

e 20 phi (10 /^1 - 2.6755

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res.stacked x θ.g x t.init t.final lele / t.req t.req θ.a t.req 0 2 2 mat 0 t.req θ.a t.req t.req θ.a 2 2 mat t.req t.req θ.a 1 2 mat 0 θ.a.cr θ.a.cr t θ.a.cr 2 2 mat θ.a.cr t θ.a.cr θ.a.cr t 0 2 2 mat θ.a.cr t θ.a.cr 1 2 mat 8 1 sys

e 735 phi (10 /^1 - 0.1213